Domain decomposition methods for the numerical solution of partial differential equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Series: | Lecture notes in computational science and engineering
61 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 711 - 760 |
| Physical Description: | XIII, 764 S. |
| ISBN: | 9783540772057 |
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MARC
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| 100 | 1 | |a Mathew, Tarek P. A. |e Verfasser |0 (DE-588)135628962 |4 aut | |
| 245 | 1 | 0 | |a Domain decomposition methods for the numerical solution of partial differential equations |c Tarek P. A. Mathew |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XIII, 764 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in computational science and engineering |v 61 | |
| 500 | |a Literaturverz. S. 711 - 760 | ||
| 650 | 4 | |a Decomposition method | |
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
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Record in the Search Index
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| adam_text | Contents
1
Decomposition
Frameworks................................ 1
1.1 Hybrid
Formulations.....................................
2
1.2 Schwarz Framework...................................... 9
1.3
Steklov-Poincaré
Framework.............................. 16
1.4 Lagrange
Multiplier
Framework........................... 27
1.5
Least Squares-Control
Framework......................... 36
2 Schwarz Iterative
Algorithms
.............................. 47
2.1
Background
............................................. 48
2.2
Projection Formulation of
Schwarz
Algorithms
.............. 56
2.3
Matrix Form of
Schwarz Subspace
Algorithms
.............. 66
2.4
Implementational Issues
.................................. 72
2.5
Theoretical Results
...................................... 77
3 Schur
Complement and Iterative
Substructuring Algorithms
................................107
3.1
Background
.............................................108
3.2 Schur
Complement System
...............................110
3.3
FFT Based Direct Solvers
................................125
3.4
Two
Subdomain
Preconditioners
..........................140
3.5
Preconditioners in Two Dimensions
........................155
3.6
Preconditioners in Three Dimensions
,......................162
3.7
Neumann-Neumann and Balancing Preconditioners
..........175
3.8
Implementational Issues
..................................185
3.9
Theoretical Results
......................................192
4 Lagrange
Multiplier Based Substructuring:
FETI
Method
.............................................231
4.1
Constrained Minimization Formulation
.....................232
4.2 Lagrange
Multiplier Formulation
___...................... 239
4.3
Projected Gradient Algorithm
.............................241
4.4
FETI-DP and BDDC Methods
............................250
XII Contents
5
Computational Issues and Parallelization
..................263
5.1
Algorithms for Automated Partitioning of Domains
..........264
5.2
Parallelizabiłity
of Domain Decomposition Solvers
...........280
6
Least Squares-Control Theory: Iterative Algorithms
......295
6.1
Two Overlapping
Subdomains
.............................296
6.2
Two Non-Overlapping
Subdomains
........................303
6.3
Extensions to Multiple Subdomains
........................310
7
Multilevel and Local Grid Refinement Methods
...........313
7.1
Multilevel Iterative Algorithms
............................314
7.2
Iterative Algorithms for Locally Refined Grids
..............321
8
Non-Self Adjoint Elliptic Equations: Iterative Methods
___333
8.1
Background
.............................................334
8.2
Diffusion Dominated Case
................................340
8.3
Advection Dominated Case
...............................348
8.4
Time Stepping Applications
..............................364
8.5
Theoretical Results
......................................366
9
Parabolic Equations
.......................................377
9.1
Background
.............................................378
9.2
Iterative Algorithms
.....................................381
9.3
Non-Iterative Algorithms
.................................384
9.4 Parareal-Multiple
Shooting Method
........................401
9.5
Theoretical Results
.....................................408
10
Saddle Point Problems
....................................417
10.1
Properties of Saddle Point Systems
........................418
10.2
Algorithms Based on Duality
.............................426
10.3
Penalty and Regularization Methods
.......................434
10.4
Projection Methods
......................................437
10.5
Krylov Space and Block Matrix Methods
...................445
10.6
Applications to the Stokes and Navier-Stokes Equations
......456
10.7
Applications to Mixed Formulations of Elliptic Equations
.....474
10.8
Applications to Optimal Control Problems
..................489
11
Non-Matching Grid Discretizations
........................515
11.1
Multi-Subdomain Hybrid Formulations
.....................516
11.2
Mortar Element Discretization: Saddle Point Approach
.......523
11.3
Mortar Element Discretization: Nonconforming Approach
.....551
11.4 Schwarz
Discretizations on Overlapping Grids
...............555
11.5
Alternative Nonmatching Grid Discretization Methods
.......559
11.6
Applications to Parabolic Equations
.......................564
Contents XIII
12
Heterogeneous Domain Decomposition Methods
...........575
12.1
Steklov-Poincaré
Heterogeneous Model
.....................576
12.2 Schwarz
Heterogeneous Models
............................585
12.3
Least Squares-Control Heterogeneous Models
...............589
12.4
χ
-Formulation
..........................................
594
12.5
Applications to Parabolic Equations
.......................603
13
Fictitious Domain and Domain Imbedding Methods
.......607
13.1
Background
.............................................608
13.2
Preconditioners for Neumann Problems
....................610
13.3
Preconditioners for Dirichlet Problems
.....................611
13.4 Lagrange
Multiplier and Least Squares-Control Solvers
.......614
14
Variational Inequalities and Obstacle Problems
............621
14.1
Background
.............................................622
14.2
Projected Gradient and Relaxation Algorithms
..............628
14.3 Schwarz
Algorithms for Variational Inequalities
.............633
14.4
Monotone Convergence of
Schwarz
Algorithms
..............636
14.5
Applications to Parabolic Variational Inequalities
............644
15
Maximum Norm Theory
...................................647
15.1
Maximum Principles and Comparison Theorems
.............648
15.2
Well Posedness of the
Schwarz
Hybrid Formulation
..........659
15.3
Convergence of
Schwarz
Iterative Algorithms
................661
15.4
Analysis of
Schwarz Nonmatching
Grid Discretizations
.......668
15.5
Analysis of
Schwarz
Heterogeneous Approximations
..........674
15.6
Applications to Parabolic Equations
.......................677
16
Eigenvalue Problems
.......................................679
16.1
Background
.............................................680
16.2
Gradient and Preconditioned Gradient Methods
.............682
16.3 Schur
Complement Methods
..............................683
16.4 Schwarz Subspace
Methods
...............................684
16.5
Modal Synthesis Method
.................................686
17
Optimization Problems
....................................689
17.1
Traditional Algorithms
...................................690
17.2 Schwarz
Minimization Algorithms
.........................697
18
Helmholtz Scattering Problem
.............................699
18.1
Background
.............................................700
18.2
Non-Overlapping and Overlapping Subdomain Methods
......701
18.3
Fictitious Domain and Control Formulations
................704
18.4
Hubert Uniqueness Method for Standing Waves
.............705
References
.....................................................711
Index
..........................................................761
|
| adam_txt |
Contents
1
Decomposition
Frameworks. 1
1.1 Hybrid
Formulations.
2
1.2 Schwarz Framework. 9
1.3
Steklov-Poincaré
Framework. 16
1.4 Lagrange
Multiplier
Framework. 27
1.5
Least Squares-Control
Framework. 36
2 Schwarz Iterative
Algorithms
. 47
2.1
Background
. 48
2.2
Projection Formulation of
Schwarz
Algorithms
. 56
2.3
Matrix Form of
Schwarz Subspace
Algorithms
. 66
2.4
Implementational Issues
. 72
2.5
Theoretical Results
. 77
3 Schur
Complement and Iterative
Substructuring Algorithms
.107
3.1
Background
.108
3.2 Schur
Complement System
.110
3.3
FFT Based Direct Solvers
.125
3.4
Two
Subdomain
Preconditioners
.140
3.5
Preconditioners in Two Dimensions
.155
3.6
Preconditioners in Three Dimensions
,.162
3.7
Neumann-Neumann and Balancing Preconditioners
.175
3.8
Implementational Issues
.185
3.9
Theoretical Results
.192
4 Lagrange
Multiplier Based Substructuring:
FETI
Method
.231
4.1
Constrained Minimization Formulation
.232
4.2 Lagrange
Multiplier Formulation
_. 239
4.3
Projected Gradient Algorithm
.241
4.4
FETI-DP and BDDC Methods
.250
XII Contents
5
Computational Issues and Parallelization
.263
5.1
Algorithms for Automated Partitioning of Domains
.264
5.2
Parallelizabiłity
of Domain Decomposition Solvers
.280
6
Least Squares-Control Theory: Iterative Algorithms
.295
6.1
Two Overlapping
Subdomains
.296
6.2
Two Non-Overlapping
Subdomains
.303
6.3
Extensions to Multiple Subdomains
.310
7
Multilevel and Local Grid Refinement Methods
.313
7.1
Multilevel Iterative Algorithms
.314
7.2
Iterative Algorithms for Locally Refined Grids
.321
8
Non-Self Adjoint Elliptic Equations: Iterative Methods
_333
8.1
Background
.334
8.2
Diffusion Dominated Case
.340
8.3
Advection Dominated Case
.348
8.4
Time Stepping Applications
.364
8.5
Theoretical Results
.366
9
Parabolic Equations
.377
9.1
Background
.378
9.2
Iterative Algorithms
.381
9.3
Non-Iterative Algorithms
.384
9.4 Parareal-Multiple
Shooting Method
.401
9.5
Theoretical Results
.408
10
Saddle Point Problems
.417
10.1
Properties of Saddle Point Systems
.418
10.2
Algorithms Based on Duality
.426
10.3
Penalty and Regularization Methods
.434
10.4
Projection Methods
.437
10.5
Krylov Space and Block Matrix Methods
.445
10.6
Applications to the Stokes and Navier-Stokes Equations
.456
10.7
Applications to Mixed Formulations of Elliptic Equations
.474
10.8
Applications to Optimal Control Problems
.489
11
Non-Matching Grid Discretizations
.515
11.1
Multi-Subdomain Hybrid Formulations
.516
11.2
Mortar Element Discretization: Saddle Point Approach
.523
11.3
Mortar Element Discretization: Nonconforming Approach
.551
11.4 Schwarz
Discretizations on Overlapping Grids
.555
11.5
Alternative Nonmatching Grid Discretization Methods
.559
11.6
Applications to Parabolic Equations
.564
Contents XIII
12
Heterogeneous Domain Decomposition Methods
.575
12.1
Steklov-Poincaré
Heterogeneous Model
.576
12.2 Schwarz
Heterogeneous Models
.585
12.3
Least Squares-Control Heterogeneous Models
.589
12.4
χ
-Formulation
.
594
12.5
Applications to Parabolic Equations
.603
13
Fictitious Domain and Domain Imbedding Methods
.607
13.1
Background
.608
13.2
Preconditioners for Neumann Problems
.610
13.3
Preconditioners for Dirichlet Problems
.611
13.4 Lagrange
Multiplier and Least Squares-Control Solvers
.614
14
Variational Inequalities and Obstacle Problems
.621
14.1
Background
.622
14.2
Projected Gradient and Relaxation Algorithms
.628
14.3 Schwarz
Algorithms for Variational Inequalities
.633
14.4
Monotone Convergence of
Schwarz
Algorithms
.636
14.5
Applications to Parabolic Variational Inequalities
.644
15
Maximum Norm Theory
.647
15.1
Maximum Principles and Comparison Theorems
.648
15.2
Well Posedness of the
Schwarz
Hybrid Formulation
.659
15.3
Convergence of
Schwarz
Iterative Algorithms
.661
15.4
Analysis of
Schwarz Nonmatching
Grid Discretizations
.668
15.5
Analysis of
Schwarz
Heterogeneous Approximations
.674
15.6
Applications to Parabolic Equations
.677
16
Eigenvalue Problems
.679
16.1
Background
.680
16.2
Gradient and Preconditioned Gradient Methods
.682
16.3 Schur
Complement Methods
.683
16.4 Schwarz Subspace
Methods
.684
16.5
Modal Synthesis Method
.686
17
Optimization Problems
.689
17.1
Traditional Algorithms
.690
17.2 Schwarz
Minimization Algorithms
.697
18
Helmholtz Scattering Problem
.699
18.1
Background
.700
18.2
Non-Overlapping and Overlapping Subdomain Methods
.701
18.3
Fictitious Domain and Control Formulations
.704
18.4
Hubert Uniqueness Method for Standing Waves
.705
References
.711
Index
.761 |
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| id | DE-604.BV023485676 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:39:30Z |
| indexdate | 2024-07-09T21:19:51Z |
| institution | BVB |
| isbn | 9783540772057 |
| language | English |
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| series | Lecture notes in computational science and engineering |
| series2 | Lecture notes in computational science and engineering |
| spelling | Mathew, Tarek P. A. Verfasser (DE-588)135628962 aut Domain decomposition methods for the numerical solution of partial differential equations Tarek P. A. Mathew Berlin [u.a.] Springer 2008 XIII, 764 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in computational science and engineering 61 Literaturverz. S. 711 - 760 Decomposition method Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Gebietszerlegungsmethode (DE-588)4309232-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Gebietszerlegungsmethode (DE-588)4309232-9 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-77209-5 Lecture notes in computational science and engineering 61 (DE-604)BV011386476 61 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016667731&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathew, Tarek P. A. Domain decomposition methods for the numerical solution of partial differential equations Lecture notes in computational science and engineering Decomposition method Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Gebietszerlegungsmethode (DE-588)4309232-9 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4309232-9 |
| title | Domain decomposition methods for the numerical solution of partial differential equations |
| title_auth | Domain decomposition methods for the numerical solution of partial differential equations |
| title_exact_search | Domain decomposition methods for the numerical solution of partial differential equations |
| title_exact_search_txtP | Domain decomposition methods for the numerical solution of partial differential equations |
| title_full | Domain decomposition methods for the numerical solution of partial differential equations Tarek P. A. Mathew |
| title_fullStr | Domain decomposition methods for the numerical solution of partial differential equations Tarek P. A. Mathew |
| title_full_unstemmed | Domain decomposition methods for the numerical solution of partial differential equations Tarek P. A. Mathew |
| title_short | Domain decomposition methods for the numerical solution of partial differential equations |
| title_sort | domain decomposition methods for the numerical solution of partial differential equations |
| topic | Decomposition method Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Gebietszerlegungsmethode (DE-588)4309232-9 gnd |
| topic_facet | Decomposition method Differential equations, Partial Numerical solutions Partielle Differentialgleichung Gebietszerlegungsmethode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016667731&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011386476 |
| work_keys_str_mv | AT mathewtarekpa domaindecompositionmethodsforthenumericalsolutionofpartialdifferentialequations |